You might start by looking at the Livecode Quality Center to Linix bugs that are reported and not resolved or closed. I am not sure I did the search right as I only get 30 bugs and most are very, very old:
ID Product Comp Assignee Status Resolution Summary Changed
6367 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Comboboxes not rendered correctly under KDE 2011-03-02
9191 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- LiveCode externals need SELinux exceptions added 2010-11-23
2782 Revoluti Engine >
ideteam@runrev.com CONFIRMED --- Windowboundingrect is set incorrectly by the IDE under Gnome 2010-07-12
2965 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Can't set the iconic property of a stack with a WindowSha... 2006-06-12
10031 Revoluti Engine >
sebastien.nouat@livecode.com HIBERNATED --- some valid date values not recognized as dates 2013-08-20
7225 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- whilst connected to chatrev IDE became totally unresponsive 2014-08-22
10334 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Can't drop to desktop on Linux 2015-03-19
5782 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Option menu buttons under GNOME don't look and behave as ... 2016-07-12
5789 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Changing the resizable property for a window changes its ... 2008-10-05
7468 Revoluti Engine >
fraser.gordon@livecode.com IN_PROGRESS --- diskSpace function always returns 1 on Linux 2014-08-08
5901 Revoluti Engine >
engineteam@runrev.com REOPENED --- Popup menus don't notify their source button correctly 2008-06-27
5909 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- hostnameToAddress doesn't work properly in linux 2018-04-22
8552 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- format does not honor "0" flag in format string 2019-02-20
2505 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Gnome icon support 2011-03-02
6640 Revoluti Unclassi
ideteam@runrev.com CONFIRMED --- Rules for setting IDE defaultFolder 2008-06-26
9370 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- need more control over the appearance of selected text 2014-03-12
2920 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Window Icon 2005-06-22
9386 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- dragImage for Linux 2018-09-07
1118 Revoluti Engine >
tuviah@runrev.com CONFIRMED --- Support for other signals 2004-03-09
8133 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Enhance 'replace' to work like s/ in Sed - line by line,... 2009-06-26
6034 Revoluti IDE > GU
ideteam@runrev.com CONFIRMED --- User Extensions location not intuitive 2015-07-29
2256 Revoluti Engine >
tuviah@runrev.com CONFIRMED --- GConf registry editor 2010-07-12
7220 Revoluti IDE > GU
ideteam@runrev.com CONFIRMED --- change button and no button type appears in inspector 2016-04-21
8553 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- resumeStack not sent to stack after modal dialog closes 2020-06-26
7018 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Special folder path "Desktop" throws an error 2016-04-21
7146 Revoluti Engine >
engineteam@runrev.com UNCONFIRMED --- Bad beheavior of Revolution 2.9/3.0 with mplayer 2016-04-21
3372 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Read from serial line hangs under Linux 2016-04-21
7233 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- standalone played sound yesterday, doesn't play today 2016-04-21
7654 Revoluti Engine >
engineteam@runrev.com CONFIRMED --- Command-keys for switching between windows of an applicat... 2016-04-21
1352 Revoluti Engine >
engineteam@runrev.com IN_PROGRESS --- Some audio files do not play via audioclips under linux. 2016-04-21
Still, it would be a place to start to see what engine bits do not work or work as expected under Linux.